I Testing superposition of spacetime curvature

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The discussion focuses on the theoretical feasibility of testing the superposition of spacetime curvature, akin to Bell's theorem, by detecting particle locations in superposition. It highlights the challenges of conducting such experiments, particularly the need for both heavy objects and delocalized states to achieve entanglement while ensuring gravity is the dominant force. Preliminary proposals suggest methods for exploring the quantum nature of gravity, including one that introduces an inequality related to quantum gravitational interactions. The conversation emphasizes that while the theoretical framework exists, the technological means to conduct these tests are currently limited. Overall, the exploration of these concepts could significantly advance our understanding of quantum gravity.
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Analogous to Bell's theorem testing: for particle in superposition of locations detecting spacetime curvature to test if spacetime can be in superposition
How is humanity technologically ready for testing below:
Something analogous to Bell's theorem testing: for particle(s) in superposition of locations detecting spacetime curvature to test if spacetime can be in superposition.
Does above test make sense theoretically even if far from technologically feasible?
 
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https://physics.aps.org/articles/v10/s138
Some preliminary proposals for testing the quantum nature of gravity by seeing if it can be used to entangle two particles. Such experiments are challenging because you need both heavy objects (to ensure gravity is the dominant force) and delocalized states (to ensure entanglement). These two properties are hard to obtain simultaneously.

[edit] - https://arxiv.org/pdf/1707.06036 : A recent proposal that was published in PRL

https://journals.aps.org/prx/abstract/10.1103/PhysRevX.14.021022
An alternative experiment proposal that avoids the above problem. The authors identify an inequality, an upper bound on the inequality, and the implication of a violation of that bound: quantum gravitational interaction.
 
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For the quantum state ##|l,m\rangle= |2,0\rangle## the z-component of angular momentum is zero and ##|L^2|=6 \hbar^2##. According to uncertainty it is impossible to determine the values of ##L_x, L_y, L_z## simultaneously. However, we know that ##L_x## and ## L_y##, like ##L_z##, get the values ##(-2,-1,0,1,2) \hbar##. In other words, for the state ##|2,0\rangle## we have ##\vec{L}=(L_x, L_y,0)## with ##L_x## and ## L_y## one of the values ##(-2,-1,0,1,2) \hbar##. But none of these...

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